Constant engagement characteristic for a gear rack pair

Abstract

The application discloses a constant engagement characteristic pair-gear-rack pair, and relates to the technical field of gear transmission, comprising a pair-gear rack based on conjugate curves and a pair-gear cylindrical gear. In the application, the normal tooth profile curve of the pair-gear cylindrical gear and the pair-gear rack is a continuous combination curve with the same curve shape, which is convenient for processing with the same cutter; the common normal line at the inflection point or the tangent point of the continuous combination curve passes through the node of the gear rack pair, and the inflection point or the tangent point position can be adjusted according to requirements to adjust the sliding rate of the gear rack pair; the pair-gear rack pair can be designed in a symmetrical form along the tooth width, and the overlap degree is designed as an integer, so that the engagement force action line and the engagement stiffness are constant. In the application, the normal tooth profile of the pair-gear rack and the pair-gear cylindrical gear is the same, the curvature radius of the engagement point is constant and tends to infinity, the sliding rate is constant, the engagement stiffness is constant, and the direction of the engagement force action line is constant, and the application has the technical characteristics of low manufacturing cost, high bearing capacity, high transmission efficiency and low vibration and noise.

Description

Technical Field

[0001] This invention relates to a pair of gear racks with constant meshing characteristics having the same continuous combined curve tooth profile, and more particularly to a pair of gear racks consisting of a pair of racks and a pair of cylindrical gears with the same normal tooth profile, a constant and infinitumimetric radius of curvature at the meshing point, a constant sliding rate, a constant meshing stiffness, and a constant direction of the meshing force line of action. Background Technology

[0002] Rack and pinion drives are one of the main forms of mechanical transmission. Their function is to realize the mutual conversion and power transmission between the rotary motion of cylindrical gears and the linear motion of racks, and they are applied in aerospace, industrial automation equipment, precision instruments, and other fields. Existing rack and pinion pairs are mostly involute rack and pinion pairs, which suffer from problems such as high slip ratio between tooth surfaces, time-varying meshing stiffness, and time-varying lines of action of meshing forces. These problems are difficult to solve, leading to reduced transmission efficiency, shortened service life, and decreased dynamic meshing performance. With the development of technology and the expansion of applications, traditional rack and pinion pairs can no longer meet the needs of industrial production and daily life.

[0003] Two patents, publication numbers 103939575A and 105202115A, disclose point-contact gear meshing pairs based on conjugate curves. The gear pairs constructed in these two patents consist of a convex gear and a concave gear. The pair of convex and concave teeth in the gear pair requires different cutting tools, increasing the manufacturing cost of the gear pair. The concave and convex tooth shape limits the radius of curvature at the meshing point, thus restricting further improvement in the load-bearing capacity of the gear pair. Selecting the contact point at the node causes tooth surface interference, making it difficult to achieve zero slip rate. During meshing, the movement of the contact point in the tooth width direction leads to time-varying meshing force. Therefore, there is an urgent need to innovate tooth profile design based on the existing spatial conjugate curve gear design theory to improve the meshing performance of gear-rack transmissions and reduce the production cost of gear-rack transmissions. Summary of the Invention

[0004] In view of this, the present invention overcomes the defects of the prior art and proposes a constant meshing characteristic gear rack pair, which includes a rack and a cylindrical gear. The rack and the cylindrical gear have the same normal tooth profile, the radius of curvature at the meshing point is constant and tends to infinity, the sliding ratio is constant, and the meshing stiffness is constant. It has the technical characteristics of low manufacturing cost, high load-bearing capacity, high transmission efficiency, and low vibration and noise.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] This invention provides a constant meshing characteristic gear rack pair, comprising a paired rack and a paired cylindrical gear based on a conjugate curve; characterized in that the normal tooth profile curve Γ of the paired rack in the constant meshing characteristic gear rack pair... s1 The normal tooth profile curve Γ of the cylindrical gear s2 Γ is a continuous combination of curves with the same shape. L The continuous combination curve Γ L The combined curve Γ, including odd-power function curves and their tangents at inflection points. L1 The curve Γ is a combination of a sine function curve and its tangent at its inflection point. L2 The combined curve of the epicycloid function curve and its tangent at the inflection point Γ L3 Combination curves of odd-power functions Γ L4 The combination curve of sine functions Γ L5 Or the combined curve Γ of the epicycloid function L6 The continuous combination curve Γ L It consists of two continuous curves, and the connection point between the two continuous curves is the inflection point or tangent point of the continuous composite curve. The continuous composite curve Γ L The common normal at the inflection point or tangent point passes through the node of the gear rack pair; the normal tooth profile curve is swept along the given conjugate curve to obtain the tooth surface of the paired rack and the paired cylindrical gear.

[0007] Optionally, when the continuous combination curve Γ L Γ is a combination curve of an odd-power function curve and its tangent at its inflection point. L1 At that time, the continuous combination curve Γ L The tangent line Γ at the inflection point of the odd power function curve L11 And odd power function curve Γ L12 Composition; A rectangular coordinate system is established at the tangent points of the continuous combined curves, and the combined curve Γ of the odd-power function curve and its tangents at the inflection points. L1 The equation is:

[0008]

[0009] In the formula: x 10 and y 10 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of values ​​for the continuous curve; A is the coefficient of the equation; and n is the degree of the independent variable and is a positive integer.

[0010] Optionally, when the continuous combination curve Γ L Γ is a combination curve of a sine function curve and its tangents at inflection points. L2 At that time, the continuous combination curve Γ L The tangent Γ at the inflection point of the sine function curveL21 and the sine function curve Γ L22 Composition; A rectangular coordinate system is established at the tangent points of the continuous composite curves, and the composite curve Γ of the sine function curve and its tangents at the inflection points. L2 The equation is:

[0011]

[0012] In the formula: x 20 and y 20 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent line at the inflection point of the sine function curve; A and B are the coefficients of the equation.

[0013] Optionally, when the continuous combination curve Γ L Γ is a combination curve of the epicycloid function curve and its tangent at the inflection point. L3 At that time, the continuous combination curve Γ L The tangent Γ at the inflection point of the epicycloid function curve L31 and the epicycloid function curve Γ L32 Composition; A rectangular coordinate system is established at the tangent points of the continuous composite curves, and the composite curve Γ of the epicycloid function curve and its tangents at the inflection points. L3 The equation is:

[0014]

[0015] In the formula: x 30 and y 30 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent at the inflection point of the epicycloid function curve; R and r are the radii of the moving and fixed circles of the cycloid, respectively; and e is the eccentricity.

[0016] Optionally, when the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 At that time, the continuous combination curve Γ L From the curve Γ of the first odd power function L41 Curve of the second odd power function Γ L42 Composition; Establish a rectangular coordinate system at the inflection points of the continuous combination curve, the combination curve Γ of the odd power function. L4 The equation is:

[0017]

[0018] In the formula: x 40 and y 40t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; A and B are the coefficients of the equation; n1 and n2 are the positive integers of the degree of the independent variable.

[0019] Optionally, when the continuous combination curve Γ L The combination curve Γ of the sine function L5 At that time, the continuous combination curve Γ L From the first sine function curve Γ L51 The second sine function curve Γ L52 Composition; Establish a rectangular coordinate system at the inflection points of the continuous combination curve, the combination curve Γ of the sine function L5 The equation is:

[0020]

[0021] In the formula: x 50 and y 50 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; parameter t is the independent variable of the equation; t1 and t2 are the range of values ​​for the continuous curve; A1, B1, A2, and B2 are the coefficients of the equation.

[0022] Optionally, when the continuous combination curve Γ L The combined curve Γ of the epicycloid function L6 At that time, the continuous combination curve Γ L From the first epicycloid function curve Γ L61 Second epicycloid function curve Γ L62 Composition; a rectangular coordinate system is established at the inflection points of the continuous composite curve, and the composite curve Γ of the epicycloid function is... L6 The equation is:

[0023]

[0024] In the formula: x 60 and y 60 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; R1 and r1 are the radii of the moving circle and the fixed circle of the first epicycloid, respectively; R2 and r2 are the radii of the moving circle and the fixed circle of the second epicycloid, respectively; e is the eccentricity.

[0025] Optionally, the continuous combination curve Γ L Rotating the rack by an angle α1 about the origin of the rectangular coordinate system yields the normal tooth profile curve Γ. s1 The equation of the curve is:

[0026]

[0027] In the formula: x 01 and y 01 These are the x and y coordinates of the normal tooth profile curve of the rack in a rectangular coordinate system.

[0028] Optionally, the normal tooth profile curve Γ of the paired rack is... s1 The normal tooth profile curve Γ of the paired cylindrical gears is obtained by rotating the gears by 180° around the origin of the rectangular coordinate system. s2 The equation of the curve is:

[0029]

[0030] In the formula: x 02 and y 02 These are the x and y coordinates of the normal tooth profile curve of the paired cylindrical gear in a rectangular coordinate system.

[0031] Optionally, the normal tooth profile curve Γ of the paired rack is... s1 The tooth surface Σ1 of the paired rack is obtained by sweeping along a given helix, and the tooth surface equation is:

[0032]

[0033] In the formula: x Σ1 y Σ1 and z Σ1 These are the coordinate values ​​of the tooth surfaces of the rack and pinion; β is the helix angle of the gear pair; parameter m is the independent variable of the equation; and m1 and m2 are the ranges of the tooth width.

[0034] Optionally, the normal tooth profile curve Γ of the paired cylindrical gears s2 The tooth surface Σ2 of the paired cylindrical gear is obtained by sweeping along a given helix, and the tooth surface equation is:

[0035]

[0036] In the formula: x Σ2 y Σ2 and z Σ2 θ represents the coordinates of the tooth surfaces of the paired cylindrical gears; r is the pitch circle radius of the paired gear rack pair with constant meshing characteristics; and θ is the angle of the given contact line.

[0037] Optionally, the contact ratio of the gear rack pair can be designed to be an integer to achieve constant stiffness meshing transmission.

[0038] Optionally, the paired rack and the paired cylindrical gear can be designed to be symmetrical along the tooth width to achieve a constant line of action of the meshing force of the gear rack pair.

[0039] The present invention achieves the following technical effects compared to the prior art:

[0040] In this invention, the normal tooth profiles of the rack and the cylindrical gear are the same, allowing them to be machined with the same tool, thus reducing manufacturing costs. The radius of curvature at the meshing point is constant and tends to infinity, improving the load-bearing capacity of the gear rack pair. The slip ratio is constant during meshing and can be designed to be zero, improving the transmission efficiency of the gear rack pair and reducing wear during transmission. The rack and cylindrical gear can be designed to be symmetrical along the tooth width, achieving a constant line of action of the meshing force. The overlap ratio of the gear rack pair is designed to be an integer, achieving constant meshing stiffness, thereby greatly reducing the vibration and noise of the gear rack pair. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a schematic diagram of a curve combining an odd-power function curve and its tangent at its inflection point, provided in the first embodiment of the present invention.

[0043] Figure 2 A schematic diagram of the formation of the normal tooth profile of a gear rack pair using a combination curve of an odd power function curve and its tangent at the inflection point as a constant meshing characteristic of the same tooth profile curve, provided for the first embodiment of the present invention.

[0044] Figure 3 A schematic diagram of the construction of the tooth surface of a gear rack pair with a combination curve of an odd power function curve and its tangent at the inflection point, provided for the first embodiment of the present invention, as a constant meshing characteristic of the same tooth profile curve;

[0045] Figure 4 A schematic diagram of a gear rack pair with constant meshing characteristics based on an odd power function curve and its tangent at the inflection point, provided as a first embodiment of the present invention;

[0046] Figure 5 A schematic diagram of the radius of curvature at the meshing point of a gear rack pair, which is a combination curve of an odd power function curve and its tangent at the inflection point, provided as a constant meshing characteristic of the same tooth profile curve, in the first embodiment of the present invention.

[0047] Figure 6 A schematic diagram of a designated point on the line of action of the meshing force of a gear rack pair with the same continuous combined curve tooth profile, provided for the first embodiment of the present invention;

[0048] Figure 7A schematic diagram of the slip ratio at the meshing point of a gear rack pair, provided as a combination curve of an odd power function curve and its tangent at the inflection point, for the constant meshing characteristics of the same tooth profile curve, provided in the first embodiment of the present invention.

[0049] Figure 8 This is a schematic diagram of a herringbone gear rack pair with constant meshing characteristics provided in the second embodiment of the present invention;

[0050] Figure 9 This is a schematic diagram of the meshing force of the herringbone gear rack pair based on the constant meshing characteristics in the second embodiment of the present invention.

[0051] Explanation of reference numerals in the attached drawings: 1. Paired rack; 2. Paired cylindrical gear. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] The following is in conjunction with the appendix Figure 1-9 The present invention will be described in further detail below.

[0054] In a constant meshing characteristic gear rack pair disclosed in this invention, the normal tooth profile curves of the rack 1 and the cylindrical gear 2 are continuous combination curves with the same curve shape, and the meshing point of the rack 1 and the cylindrical gear 2 is at the inflection point or tangent point of the continuous combination curve.

[0055] In the first embodiment of the present invention, the basic parameters of the constant meshing characteristic gear rack pair are: module m = 8, number of teeth of the gear pair z1 = 20, and addendum coefficient h. a * = 0.5, clearance coefficient c* = 0.2, addendum h a =4mm, tooth root height h f =5.6mm, helix angle β=15°, tooth width w=40mm.

[0056] Taking the curve of an odd-power function and the combination curve of its tangent at its inflection point as an example, in the rectangular coordinate system σ1(O 1-x1 Plot the curve of the odd-power function and the combination curve of the tangent lines at its inflection points on the graph y1, as shown below. Figure 1 As shown. Taking coefficients A = 1.2 and n = 2, the combined curve Γ of the odd-power function curve and its tangent at the inflection point is... L1 (The tangent line Γ at the inflection point of the odd power function curve) L11 And odd power function curve Γ L12The equation for the composition is:

[0057]

[0058] In the formula: x 10 and y 10 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system σ1, respectively; parameter t is the independent variable of the equation; t1 and t2 are the ranges of values ​​for the continuous curve.

[0059] The first embodiment of this invention provides a schematic diagram of the normal tooth profile formation of a gear rack pair using a combination curve of an odd-power function curve and its tangent at the inflection point as the tooth profile curve. The inflection point P is the meshing point, as shown in the diagram. Figure 2 As shown in the figure, the tooth roots of both the rack 1 and the cylindrical gear 2 are tangent segments, while the tooth roots of both the rack 1 and the cylindrical gear 2 are cubic power function curve segments. When the continuous combined curve Γ... L Rotating the rack 1 by an angle α1 about the origin of the rectangular coordinate system yields the normal tooth profile curve Γ. s1 When rotating, the value of the rotation angle α1 needs to be determined based on the specific parameters of the gear pair, and the general range is: 0° < α1 < 180°. The specific formation process and tooth profile curve equation of the gear-rack pair are as follows:

[0060] The curve Γ is a combination of the curve of an odd power function and the tangent at its inflection point. L1 Rotating the tooth profile Γ of rack 1 by an angle α1 = 120° around the origin of the rectangular coordinate system σ1 yields the normal tooth profile curve Γ. s1 The equation of the curve is:

[0061]

[0062] In the formula: x 01 and y 01 These are the x and y coordinates of the normal tooth profile curve of rack 1 in the rectangular coordinate system σ1.

[0063] The normal tooth profile curve Γ of the tooth rack 1 s1 The normal tooth profile curve Γ of the paired cylindrical gear 2 is obtained by rotating it by 180° around the origin of the rectangular coordinate system σ1. s2 The equation of the curve is:

[0064]

[0065] In the formula: x 02 and y 02 These are the x and y coordinates of the normal tooth profile curve of the paired cylindrical gear 2 in the rectangular coordinate system σ1.

[0066] Figure 3The first embodiment of the present invention provides a schematic diagram of the construction of the tooth surface of a gear rack pair with constant meshing characteristics, using a combination curve of an odd-power function curve and its tangent at the inflection point as the tooth profile curve. The specific construction process and tooth surface equation of the gear rack pair with constant meshing characteristics are as follows:

[0067] The normal tooth profile curve Γ of the tooth rack 1 s1 The tooth surface Σ1 of the rack 1 is obtained by sweeping along a given helix, and the tooth surface equation is:

[0068]

[0069] In the formula: x Σ1 y Σ1 and z Σ1 Let m be the coordinate value of the tooth surface of rack 1, and m be the independent variable of the equation, while m1 and m2 are the range of values ​​for the tooth width.

[0070] Similarly, the normal tooth profile curve Γ of the paired cylindrical gear 2 s2 The tooth surface Σ2 of the paired cylindrical gear 2 is obtained by sweeping along a given helix, and the tooth surface equation is:

[0071]

[0072] In the formula: x Σ2 y Σ2 and z Σ2 θ represents the coordinates of the tooth surface of the cylindrical gear 2; θ is the angle of the given contact line.

[0073] Figure 4 The first embodiment of the present invention provides a schematic diagram of a gear rack pair with constant meshing characteristics, which is a combination curve of an odd power function curve and the tangent at its inflection point. By defining the addendum circle and root circle dimensions of the gear rack 1 and the gear 2 respectively, and performing operations such as trimming, stitching, and filleting on the tooth surface, a gear rack pair with constant meshing characteristics and tooth profile with the same continuous combination curve is obtained.

[0074] In the first embodiment of the present invention, the normal tooth profile curves of the paired rack 1 and the paired cylindrical gear 2 can also be a combination curve Γ of a sine function curve and its tangent at the inflection point. L2 The combined curve of the epicycloid function curve and its tangent at the inflection point Γ L3 Combination curves of odd-power functions Γ L4 The combination curve of sine functions Γ L5 Or the combined curve Γ of the epicycloid function L6 The curve formulas are as follows:

[0075] When the continuous combination curve Γ LΓ is a combination curve of a sine function curve and its tangents at inflection points. L2 At that time, the continuous combination curve Γ L The tangent Γ at the inflection point of the sine function curve L21 and the sine function curve Γ L22 Composition; Establish a rectangular coordinate system at the tangent points of the continuous composite curve, and form the composite curve Γ of the sine function curve and its tangents at the inflection points. L2 The equation is:

[0076]

[0077] In the formula: x 20 and y 20 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent line at the inflection point of the sine function curve; A and B are the coefficients of the equation.

[0078] When the continuous combination curve Γ L Γ is a combination curve of the epicycloid function curve and its tangent at the inflection point. L3 At that time, the continuous combination curve Γ L The tangent Γ at the inflection point of the epicycloid function curve L31 and the epicycloid function curve Γ L32 Composition; Establish a rectangular coordinate system at the tangent points of the continuous composite curves, and form the composite curve Γ of the epicycloid function curve and its tangents at the inflection points. L3 The equation is:

[0079]

[0080] In the formula: x 30 and y 30 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent at the inflection point of the epicycloid function curve; R and r are the radii of the moving and fixed circles of the cycloid, respectively; and e is the eccentricity.

[0081] When the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 At that time, the continuous combination curve Γ L From the curve Γ of the first odd power function L41 Curve of the second odd power function Γ L42 Composition; Establish a rectangular coordinate system at the inflection points of continuous combination curves, and the combination curve Γ of odd-power functions. L4 The equation is:

[0082]

[0083] In the formula: x40 and y 40 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; A and B are the coefficients of the equation; n1 and n2 are the positive integers of the degree of the independent variable.

[0084] When the continuous combination curve Γ L The combination curve Γ of the sine function L5 At that time, the continuous combination curve Γ L From the first sine function curve Γ L51 The second sine function curve Γ L52 Composition; Establish a rectangular coordinate system at the inflection points of the continuous composite curve, and the composite curve Γ of the sine function. L5 The equation is:

[0085]

[0086] In the formula: x 50 and y 50 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; parameter t is the independent variable of the equation; t1 and t2 are the range of values ​​for the continuous curve; A1, B1, A2, and B2 are the coefficients of the equation.

[0087] When the continuous combination curve Γ L The combined curve Γ of the epicycloid function L6 At that time, the continuous combination curve Γ L From the first epicycloid function curve Γ L61 Second epicycloid function curve Γ L62 Composition; Establish a rectangular coordinate system at the inflection points of the continuous composite curve, and the composite curve Γ of the epicycloid function. L6 The equation is:

[0088]

[0089] In the formula: x 60 and y 60 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; R1 and r1 are the radii of the moving circle and the fixed circle of the first epicycloid, respectively; R2 and r2 are the radii of the moving circle and the fixed circle of the second epicycloid, respectively; e is the eccentricity.

[0090] In this invention, the inflection point or tangent point of the continuous composite curve is:

[0091] When a continuous combination curve is a combination curve of odd-power functions, a combination curve of sine functions, or a combination curve of epicycloid functions, the connection point of the continuous combination curve is an inflection point, that is, the boundary between concavity and convexity of the curve. The second derivative of the curve is zero at this point, and the signs of the second derivatives on both sides of this point are opposite.

[0092] When the combined curve is a combination of an odd power function curve and its tangent at the inflection point, a sine function curve and its tangent at the inflection point, or an epicycloid and its tangent at the inflection point, the connection point of the combined curve is the inflection point of the odd power function curve, sine function curve, or epicycloid (meaning the same as ①), and is also the tangent point of the tangent of the odd power function curve, sine function curve, or epicycloid at that point.

[0093] At the inflection points or tangent points of a continuous composite curve, the curvature of the curve is zero, meaning the radius of curvature tends to infinity. Specifically, when the continuous composite curve is a combination of odd-power functions, sine functions, or epicycloid functions, the radii of curvature on both sides of the inflection point tend to infinity. When the continuous composite curve is a combination of an odd-power function curve and its tangent at the inflection point, a sine function curve and its tangent at the inflection point, or an epicycloid function curve and its tangent at the inflection point, the radius of curvature on the odd-power function side of the inflection point tends to infinity, and the radius of curvature on the tangent side is infinite. The radius of curvature of the composite curve is calculated based on the parameters given in the embodiment, such as... Figure 5 As shown, the radius of curvature of the straight line segment in the composite curve is infinite; the radius of curvature at the inflection point tends to infinity, and the radius of curvature of the cubic power function curve segment gradually decreases and then increases, but is still much smaller than the radius of curvature at the inflection point; this means that the radius of curvature at the contact point of the gear rack pair with constant meshing characteristics tends to infinity, which improves the load-bearing capacity of the gear rack pair with constant meshing characteristics.

[0094] In the first embodiment of the present invention, the inflection point or tangent point of the continuous combination curve is located at a designated point on the line of action of the meshing force of the gear pair. The designated point is specifically defined as: the line of action of the meshing force of the gear rack pair with constant meshing characteristics is a straight line passing through the node and forming a certain angle (pressure angle) with the horizontal axis, and a given point on or near the node on the straight line. Figure 6 This diagram illustrates a designated point on the line of action of the meshing force of a gear pair. In the diagram: P is the designated point on the line of action of the meshing force of the gear pair; P1 and P2 are the extreme points within the position range of the designated point; the straight lines N1N2 represent the line of action of the meshing force of the gear pair; α k The pressure angle is O1, which is the center point of the opposing cylindrical gear 2. a h is the tooth tip height. fLet w1 be the tooth root height, w1 be the angular velocity of the opposing cylindrical gear 2, and v1 be the moving speed of the opposing rack 1. The specified point P is usually located at the node, but can also be a given point near both sides of the node. The variation area of ​​the specified point does not exceed half of the tooth height.

[0095] According to the gear meshing principle, there is no relative sliding between the tooth surfaces when a gear and rack pair with constant meshing characteristics meshes at the pitch point. Figure 7 This first embodiment of the invention provides a schematic diagram of the slip ratio at the meshing point of a gear rack pair with a constant meshing characteristic, using a combination curve of an odd-power function curve and its tangent at the inflection point as the tooth profile curve. Since the gear rack pair with a constant meshing characteristic, having the same continuous combined curve tooth profile, meshes at the node at any given time, this constant meshing characteristic gear rack pair can achieve zero-slip meshing. When the inflection point or tangent point of the combined curve does not coincide with the node, the slip ratio of the constant meshing characteristic gear rack pair remains constant but is not zero. The closer the inflection point or tangent point of the continuous curve is to the node, the smaller the slip ratio of the constant meshing characteristic gear rack pair, and vice versa. When the inflection point or tangent point coincides with the node, the constant meshing characteristic gear rack pair can achieve zero-slip meshing transmission, reducing wear between tooth surfaces and improving the transmission efficiency of the constant meshing characteristic gear rack pair.

[0096] Furthermore, when the contact ratio of a constant meshing characteristic gear rack pair with the same continuous combined curve tooth profile is designed to be an integer, the meshing stiffness of the constant meshing characteristic gear rack pair is constant. At this point, the meshing force of the constant meshing characteristic gear rack pair at any meshing position is determined. Therefore, when the contact ratio is designed to be an integer, the meshing state of the constant meshing characteristic gear rack pair with the same continuous combined curve tooth profile is constant at any time, effectively ensuring the stability of the dynamic meshing performance of the constant meshing characteristic gear rack pair and effectively reducing the vibration and noise of the constant meshing characteristic gear rack pair.

[0097] In the second embodiment of the present invention, the paired rack and paired cylindrical gear based on the conjugate curve are designed as symmetrical along the tooth width, i.e., herringbone teeth or arc-shaped teeth. Taking a herringbone gear rack pair with constant meshing characteristics as an example, it includes a paired herringbone rack 1 and a paired herringbone cylindrical gear 2, such as... Figure 8 As shown. Based on the normal tooth profile method, the equations of the left and right tooth surfaces of the herringbone rack can be obtained as follows:

[0098]

[0099] In the formula, the "+" sign represents the left tooth surface of the paired gear rack, and the "-" sign represents the right tooth surface. Based on the normal tooth profile method, the equations for the left and right tooth surfaces of the paired herringbone cylindrical gear can be obtained as follows:

[0100]

[0101] In the formula, the "+" sign in the ± symbol represents the left tooth surface of the gear pair, and the "-" sign represents the right tooth surface of the gear pair.

[0102] Taking the constant meshing characteristics of the herringbone gear rack pair in the second embodiment as an example, a schematic diagram of the meshing force of the gear rack pair is established, as follows: Figure 9 As shown. For the right side of the herringbone gear rack pair with constant meshing characteristics, the meshing force F on the herringbone cylindrical gear 2 is... n1 It can be decomposed into axial force F a1 Radial force F r1 and circumferential force F t1 The meshing force F on the left side of the herringbone gear rack pair is the meshing force on the herringbone cylindrical gear. n2 It can be decomposed into axial force F a2 Radial force F r2 and circumferential force F t2 When considering only the right side of the gear and rack pair, during meshing, as the meshing point moves in the tooth width direction, the meshing force F... n1 The shift in the tooth width direction and the change in force state cause periodic changes in the excitation factors of the gear-rack pair, severely affecting its dynamic meshing performance. When considering both sides of the herringbone gear-rack pair simultaneously, due to the complete symmetry of the left and right teeth, the axial force F on both sides of the tooth surface... a1 and F a2 The radial forces F on both sides cancel each other out. r1 and F r2 Simplifying to the center position along the tooth width direction of the herringbone gear rack pair, the circumferential force F on both sides is... t1 and F t2 Similarly, simplifying to the center position along the tooth width direction of the herringbone cylindrical gear, the meshing force F at any given time is... n1 and F n2 The determination of the position and direction of the line of action of the resultant force Fn improves the stability of the meshing process of the herringbone gear rack pair.

[0103] Furthermore, when the overlap ratio of the herringbone gear rack transmission with constant meshing characteristics in the second embodiment is designed to be an integer, the meshing stiffness is constant. At this time, the magnitude of the meshing force of the gear rack pair at any meshing position is determined, and the position and direction of the meshing force at any time are also determined. Therefore, the meshing state of the herringbone gear rack transmission is constant at any time, which effectively ensures the stability of the dynamic meshing performance of the herringbone gear rack pair.

[0104] It should be noted that, for those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0105] This specification uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A gear and rack pair with constant meshing characteristics, characterized in that, Including a pair of racks (1) and cylindrical gears (2) based on conjugate curves; characterized in that the normal tooth profile curve Γ of the rack (1) in the constant meshing characteristic pair of gears and racks is... s1 The normal tooth profile curve Γ of the cylindrical gear (2) s2 Γ is a continuous combination of curves with the same shape. L The continuous combination curve Γ L The combined curve Γ, which includes odd-power function curves and their tangents at inflection points. L1 Combination curves of odd-power functions Γ L4 The continuous combination curve Γ L It consists of two continuous curves, and the connection point between the two continuous curves is the inflection point or tangent point of the continuous composite curve. The continuous composite curve Γ L The common normal at the inflection point or tangent point passes through the node of the gear rack pair; the normal tooth profile curve is swept along the given conjugate curve to obtain the tooth surface of the paired rack (1) and the paired cylindrical gear (2); when the continuous combined curve Γ L Γ is a combination curve of an odd-power function curve and its tangent at its inflection point. L1 At that time, the continuous combination curve Γ L The tangent line Γ at the inflection point of the odd power function curve L11 And odd power function curve Γ L12 Composition; A rectangular coordinate system is established at the tangent points of the continuous combined curves, and the combined curve Γ of the odd-power function curve and its tangents at the inflection points. L1 The equation is: In the formula: x 10 and y 10 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of values ​​for the continuous curve; A is the coefficient of the equation; n is the degree of the independent variable and is a positive integer. When the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 At that time, the continuous combination curve Γ L From the curve Γ of the first odd power function L41 Curve of the second odd power function Γ L42 Composition; Establish a rectangular coordinate system at the inflection points of the continuous combination curve, the combination curve Γ of the odd power function. L4 The equation is: In the formula: x 40 and y 40 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; A and B are the coefficients of the equation; n1 and n2 are the positive integers of the degree of the independent variable. The continuous combination curve Γ L Rotating the rack (1) around the origin of the rectangular coordinate system by an angle α1 yields the normal tooth profile curve Γ. s1 The equation of the curve is: In the formula: x 01 and y 01 These are the x and y coordinates of the normal tooth profile curve of the rack (1) in the rectangular coordinate system.

2. A constant meshing characteristic gear rack pair according to claim 1, characterized in that: The normal tooth profile curve Γ of the rack (1) s1 The normal tooth profile curve Γ of the paired cylindrical gear (2) is obtained by rotating it by 180° around the origin of the rectangular coordinate system. s2 The equation of the curve is: In the formula: x 02 and y 02 The x and y coordinates of the normal tooth profile curve of the cylindrical gear (2) in the rectangular coordinate system are respectively.

3. A constant meshing characteristic gear rack pair according to claim 2, characterized in that: The normal tooth profile curve Γ of the rack (1) s1 The tooth surface Σ1 of the rack (1) is obtained by sweeping along a given helix, and the equation of the tooth surface is: In the formula: x Σ1 y Σ1 and z Σ1 β represents the coordinate values ​​of the tooth surface of the rack (1); β is the helix angle of the gear pair; parameter m is the independent variable of the equation; and m1 and m2 are the range of tooth width values.

4. A constant meshing characteristic gear rack pair according to claim 3, characterized in that: The normal tooth profile curve Γ of the paired cylindrical gear (2) s2 The tooth surface Σ2 of the paired cylindrical gear (2) is obtained by sweeping along a given helix, and the tooth surface equation is: In the formula: x Σ2 y Σ2 and z Σ2 θ represents the coordinate values ​​of the tooth surface of the paired cylindrical gear (2); r is the pitch circle radius of the paired gear rack pair with constant meshing characteristics; and θ is the angle of the given contact line.

5. A gear and rack pair with constant meshing characteristics according to claim 1, characterized in that: The overlap ratio of the gear rack pair is designed to be an integer to achieve constant stiffness meshing transmission.

6. A gear and rack pair with constant meshing characteristics according to claim 1, characterized in that: The paired rack (1) and the paired cylindrical gear (2) can be designed to be symmetrical along the tooth width to achieve a constant line of action of the meshing force of the gear rack pair.

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